International Portfolio Theory and Diversification
Q: What are the two components of international diversification?
A:
1. Potential for risk reduction through diversification
2. Added foreign exchange risk
Q: According to the book about ____% of the risk associated with investing in a single stock is diversifiable in a fully diversified U.S. portfolio.
A: 73%
Q: Increasing the number of securities in the portfolio reduces the ______risk of the portfolio.
A: unsystematic
Example
An investor in the U.S. takes US$1,000,000 on January 1, 2002 and invests in shares traded on the Tokyo Exchange (TSE).
On January 1, 2002 the spot rate was , so the investor received ¥130,000,000 and used this to acquire 6,500 shares at ¥20,000 each.
On January 1, 2003 the investor sold the shares at a price of ¥25,000 per share yielding ¥162,500,000 and converted the shares back to US$ at the new spot rate which resulted in $1,300,000.
To calculate the return on a cross-border investment both the change in the share price and the change in the currency value affect the total return of the portfolio. The formula for the total return in U.S. dollars is given below:
where, and
So,
Review
Beta is a measure of the extent to which the returns of a given stock move with the stock market. (i.e. “market risk”)
or
where, the Greek letter rho, (ρim), is the correlation coefficient for the stock “i” and the market “m.”
therefore, the formula for the covariance of the stock with the market “covim” is:
Remember, Beta measures only systematic risk, while standard deviation is a measure of total risk (systematic or market risk, and unsystematic risk, the risk of the security)
The calculation for the estimated standard deviation is given below:
Note: the standard deviation is the square root of the variance.
Example
Given the following information calculate the standard deviation.
Year / rt2002 / 15%
2003 / -5%
2004 / 20%
The calculation for the standard deviation of a portfolio is provided in the formula below:
where, N is the total number of assets included in the portfolio.
The calculation for the expected return of a portfolio is shown below:
Example
Calculate the standard deviation and the expected return of a portfolio with 40% invested in the following US equity and 60% invested in the following German equity index.
Expected Return / Expected Risk (σ)United States equity index (US) / 14% / 15%
German equity index (GER) / 18% / 20%
Correlation coefficient (ρUS,GER) / 0.34
Exhibit 20.6 in your book shows the possible combinations:
Source: Multinational Business Finance, 10th edition
The Sharpe ratio calculates the per unit average return over and above the risk-free rate of return for the portfolio. The Sharpe ratio measures how much excess return (return above the risk-free rate) an investor each per unit of portfolio risk.
The formula for the Sharpe measure is shown below:
The Treynor measure looks at the systematic risk of the portfolio (beta) and compares it to the world market. The formula for the Treynor measure is shown below:
Example
Given the following information calculate the Sharpe and Treynor measures
Country / Mean return / σ / rf / βHong Kong / 1.5% / 9.61% / .42% / 1.09
Note: The risk-free rate is the annual risk-free rate of 5% divided by 12, (.42%).
Q: Would the country with the highest Sharpe and Treynor measures have the best reward for the risk?
A: Yes
Questions
The following example is from pages 631-632 in your book.
An investor in the U.S. takes US$1,000,000 on January 1, 2002 and invests in shares traded on the Tokyo Exchange (TSE). On January 1, 2002 the spot rate was , so the investor received ¥130,000,000 and used this to acquire 6,500 shares at ¥20,000 each. On January 1, 2003 the investor sold the shares at a price of ¥25,000 per share yielding ¥162,500,000 and converted the shares back to US$ at the new spot rate.
Q: What would be the return if the yen had appreciated by 5%? by 10%? What does this tell you about the risk and return profile of an international asset.
Q: Given the following information calculate the Sharpe and Treynor measures of market performance:
Country / Mean return / σ / rf / βEstonia / 1.12% / 16% / .42% / 1.65
Latvia / 0.75% / 22.8% / - / 1.53
Lithuania / 1.6% / 13.5% / - / 1.20
Final Project
For your final project create a scenario analysis of the effect of stock price changes and exchange rate changes like the example in your book on pages 631-632.
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International Portfolio Theory and Diversification